What is the answer to log_{4}(2x+1)-log_{4}(x-2)=1 ?

The answer to log_{4}(2x+1)-log_{4}(x-2)=1 is x= 9/2

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log_{4}(2x+1)-log_{4}(x-2)=1

lo g_{4} (2 x + 1) - lo g_{4} (x - 2) = 1

x = \frac{9}{2}

Decimal Notation

x = 4.5

Solution steps

lo g_{4} (2 x + 1) - lo g_{4} (x - 2) = 1

Add

lo g_{4} (x - 2)

to both sides

lo g_{4} (2 x + 1) - lo g_{4} (x - 2) + lo g_{4} (x - 2) = 1 + lo g_{4} (x - 2)

Simplify

lo g_{4} (2 x + 1) = 1 + lo g_{4} (x - 2)

Apply log rules

2 x + 1 = 4 (x - 2)

Solve

2 x + 1 = 4 (x - 2) : x = \frac{9}{2}

x = \frac{9}{2}

Verify Solutions:

x = \frac{9}{2}

True

The solution is

x = \frac{9}{2}

y, 3 ln (t) - ln (y) = 4

ln (12) - ln (x - 1) = ln (x - 2)

11.5 = - lo g_{10} (x)

ln (x - 1) - 1 = - 1 + ln (- 3 x + 2)

4 ln (x + 2) = 24

What is the answer to log_{4}(2x+1)-log_{4}(x-2)=1 ?
The answer to log_{4}(2x+1)-log_{4}(x-2)=1 is x= 9/2
Solve for x: log_{4}(2x+1)-log_{4}(x-2)=1
The solution is x= 9/2